Question 1

Solve the linear equation: $$-3(6x - 17) + 18x = 8x + 51 + 3x$$

Accepted Answer

$$11$$

Question 2

Consider the set $$M = \{-1028, -2050/5, -3/25, 0, 4/21, 1, \sqrt{24}, 11, 9\pi\}. $$Which of its elements are irrational numbers?

Accepted Answer

$$\sqrt{24}, 9\pi$$

Question 3

Which of the following is the solution set for the equation $$2x - 5 = 3x + 7$$?

Accepted Answer

$$x = -12$$

Question 4

A chemist mixes two solutions, one with a concentration of $$30\%$$ and another with $$50\%$$ acid, to obtain $$10$$ liters of a $$40\%$$ acid solution. How many liters of the $$30\%$$ solution are needed?

Accepted Answer

$$5$$ liters

Question 5

Which of the following numbers is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 6

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 7

Which of the following best describes the solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 8

A medical researcher is tracking the spread of a virus. The number of cases doubles every $$3$$ days. If there are $$100$$ cases today, how many cases will there be in $$9$$ days?

Accepted Answer

$$800$$

Question 9

Which of the following is equivalent to the expression $$\frac{2x^2$ - 8}{x - 2}$$ for $$x 
eq 2$$?

Accepted Answer

Question 10

A car rental company charges a flat fee of $$\50$ plus $$\$$0.20$$ per mile driven. If a customer paid $$\90$, how many miles did they drive?

Accepted Answer

$$200$$ miles

Question 11

Which of the following is the solution to the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 12

If $$g(x) = x^2$ - 4x + 3$$, what are the zeros of $$g(x)$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 13

A population of bacteria triples every $$4$$ hours. If the initial population is $$200$$, what will the population be after $$8$$ hours?

Accepted Answer

$$1800$$

Question 14

Which of the following is the simplified form of $$\frac{4x^2$ - 9}{2x + 3}$$ for $$x 
eq -\frac{3}{2}$$?

Accepted Answer

$$2x - 3$$

Question 15

If $$h(x) = 3x - 2$$ and $$k(x) = x^2$, what is (h$$ \circ k)(2)$$?

Accepted Answer

$$10$$

Question 16

Which of the following is the domain of the function $$f(x) = \frac{1}{x - 4}$$?

Accepted Answer

$$x 
eq 4$$

Question 17

A rectangle has a length that is $$3$$ meters more than twice its width. If the perimeter is $$36$$ meters, what is the width?

Accepted Answer

$$5$$ meters

Question 18

Which of the following is the solution to the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$x = 3$$

Question 19

If $$f(x) = \sqrt{x - 1}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 1$$

Question 20

Which of the following is the solution to the system of equations: $$x + y = 7$$ and $$x - y = 3$$?

Accepted Answer

$$x = 5, y = 2$$

Linear Equations and Number Sets: College Algebra Study Notes

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